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Thermal considerations on the recalescence of alloy powders

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Abstract

The principles involved in the solidification of supercooled binary alloy droplets are discussed with particular emphasis on solute redistribution. The effects of alloying elements on the relevant parameters of the thermal history of recalescing aluminum droplets are studied with the aid of enthalpytemperature relationships. Thermal considerations indicate that the critical supercoolings to achieve partitionless solidification change rather modestly for the alloys investigated. In addition, the rate of recalescence after nucleation is likely to be slowed down by the addition of solute. A Newtonian model for solidification of nonideal binary alloys with morphologically stable interfaces is derived and used to study the thermal history and solute redistribution during recalescence. The effects of different solutes, alloy concentration, initial supercooling, and interfacial kinetics are discussed.

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Abbreviations

Bi:

Biot number,hrino LA

C:

molar heat capacity

Di :

interfacial diffusivity of solute

f, g :

molar and volume fraction solid, respectively

f a :

fraction solid that can form adiabatically below a given temperature

Fo:

Fourier number, α At/rL 20

G :

Gibbs free energy

H :

molar enthalpy

MA :

enthalpy of pure solidA at its melting temperature

AH M :

molar heat of fusion

h :

heat transfer coefficient at the droplet surface

k, k e :

interfacial and equilibrium partition coefficients, respectively

k :

thermal conductivity

R:

gas constant

r 0 :

radius of droplet or powder

Ste:

Stefan Number, AL AM G)/ΔHM/A

T :

temperature

T 0 , θ 0 :

thermodynamic limit to partitionless solidification

T :

temperature of cooling environment, 300 K

T H , θ H :

hypercooling temperature

T L , θ L :

liquidus temperature

T M :

melting temperature

T s , θ S :

solidus temperature

ΔT:

supercooling

V :

interface velocity

V o :

characteristic attachment velocity

V D :

diffusional velocity of solute atT L

X:

alloy composition in mole fraction

α :

thermal diffusivity

δi :

diffusion distance that the solute must travel to avoid trapping

θ :

dimensionless temperature; see Eq. [8]

Δθ:

dimensionless supercooling, θL -θ

k:

alloy heat capacity normalized by that of the pure solvent

μ:

chemical potential

v :

kinetic parameter,V 0 /V D

Φ :

normalized molar volume Ω/Ω AL

Ψ:

dimensionless enthalpy; see Eq. [7]

Ω :

molar volume

L :

of the liquid

N :

at the moment of nucleation

S :

of the solid

0:

relative toT o

A,B :

solvent and solute, respectively

H :

refers to enthalpy part of interaction parameter

S :

refers to entropy part of interaction parameter

x :

excess enthalpy or free energy

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Authors and Affiliations

  1. Materials Department and Department of Mechanical and Environmental Engineering, University of California, 93106, Santa Barbara, CA

    Carlos G. Levi (Assistant Professor)

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  1. Carlos G. Levi
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Levi, C.G. Thermal considerations on the recalescence of alloy powders. Metall Trans A 19, 687–697 (1988). https://doi.org/10.1007/BF02649283

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